using three.js how to add texture to .OBJ object
In your example you're creating the material but not applying it to the Mesh(es) loaded from the OBJ yet. You can do that as follows:

// Create a material
var textureLoader = new THREE.TextureLoader();
var map = textureLoader.load('./diffuse.png');
var material = new THREE.MeshPhongMaterial({map: map});

var loader = new THREE.OBJLoader();
loader.load( './my-model.obj', function ( object ) {

  // For any meshes in the model, add our material.
  object.traverse( function ( node ) {

    if ( node.isMesh ) node.material = material;

  } );

  // Add the model to the scene.
  scene.add( object );
} );


three.js r89. Documentation for THREE.OBJLoader.